Central limit theorem (cookie recipes)

Student learning outcomes

The student will demonstrate and compare properties of the central limit theorem.

Given

X = length of time (in days) that a cookie recipe lasted at the Olmstead Homestead. (Assume that each of the different recipes makes the same quantity of cookies.)

Recipe #

X

Recipe #

X

Recipe #

X

Recipe #

X

1

1

16

2

31

3

46

2

2

5

17

2

32

4

47

2

3

2

18

4

33

5

48

11

4

5

19

6

34

6

49

5

5

6

20

1

35

6

50

5

6

1

21

6

36

1

51

4

7

2

22

5

37

1

52

6

8

6

23

2

38

2

53

5

9

5

24

5

39

1

54

1

10

2

25

1

40

6

55

1

11

5

26

6

41

1

56

2

12

1

27

4

42

6

57

4

13

1

28

1

43

2

58

3

14

3

29

6

44

6

59

6

15

2

30

2

45

2

60

5

Calculate the following:

μ
x = _______

σ
x = _______

Collect the data

Use a random number generator to randomly select four samples of size
n = 5 from the given population. Record your samples in
[link] . Then, for each sample, calculate the mean to the nearest tenth. Record them in the spaces provided. Record the sample means for the rest of the class.

Complete the table:

Sample 1

Sample 2

Sample 3

Sample 4

Sample means from other groups:

Means:

x¯ = ____

x¯ = ____

x¯ = ____

x¯ = ____

Calculate the following:

x¯ = _______

sx¯ = _______

Again, use a random number generator to randomly select four samples from the population. This time, make the samples of size
n = 10. Record the samples in
[link] . As before, for each sample, calculate the mean to the nearest tenth. Record them in the spaces provided. Record the sample means for the rest of the class.

Sample 1

Sample 2

Sample 3

Sample 4

Sample means from other groups

Means:

x¯ = ____

x¯ = ____

x¯ = ____

x¯ = ____

Calculate the following:

x¯ = ______

sx¯ = ______

For the original population, construct a histogram. Make intervals with a bar width of one day. Sketch the graph using a ruler and pencil. Scale the axes.

Draw a smooth curve through the tops of the bars of the histogram. Use one to two complete sentences to describe the general shape of the curve.

Repeat the procedure for
n = 5

For the sample of
n = 5 days averaged together, construct a histogram of the averages (your means together with the means of the other groups). Make intervals with bar widths of
12 a day. Sketch the graph using a ruler and pencil. Scale the axes.

Draw a smooth curve through the tops of the bars of the histogram. Use one to two complete sentences to describe the general shape of the curve.

Repeat the procedure for
n = 10

For the sample of
n = 10 days averaged together, construct a histogram of the averages (your means together with the means of the other groups). Make intervals with bar widths of
12 a day. Sketch the graph using a ruler and pencil. Scale the axes.

Draw a smooth curve through the tops of the bars of the histogram. Use one to two complete sentences to describe the general shape of the curve.

Discussion questions

Compare the three histograms you have made, the one for the population and the two for the sample means. In three to five sentences, describe the similarities and differences.

State the theoretical (according to the clt) distributions for the sample means.

population is the whole set and the sample is the subset of population.

umair

if the data set is drawn out of a larger set it is a sample and if it is itself the whole complete set it can be treated as population.

Bhavika

hello everyone
if I have the data set which contains measurements of each part during 10 years, may I say that it's the population or it's still a sample because it doesn't contain my measurements in the future?
thanks

Alexander

Pls I hv a problem on t test is there anyone who can help?

Peggy

What's your problem Peggy Abang

Dominic

Bhavika is right

Dominic

what is the problem peggy?

Bhavika

hi

Sandeep

Hello

adeagbo

hi

Bhavika

hii Bhavika

Dar

Hi eny population has a special definition. if that data set had all of characteristics of definition, that is population. otherwise that is a sample

descriptive statistics gives you the result on the the data like you can calculate various things like variance,mean,median etc. however, inferential stats is involved in prediction of future trends using the previous stored data.

umair

if you need more help i am up for the help.

umair

Thanks a lot

Anjali

Inferential Statistics involves drawing conclusions on a population based on analysis of a sample. Descriptive statistics summarises or describes your current data as numerical calculations or graphs.

fred

my pleasure😊. Helping others offers me satisfaction 😊

umair

inferential statistics the results of the statistical analysis of the sample data of the population are used for generalization or decision making about the population
why
descriptive statistics, the analyzed data are presented without generalization or decision making about the population.